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Mat. Zametki, 2005, Volume 77, Issue 3, Pages 378–394 (Mi mz2500)  

This article is cited in 3 scientific papers (total in 3 papers)

On the $H$-property of functionals in Sobolev spaces

A. S. Leonov

Moscow Engineering Physics Institute (State University)

Abstract: In this paper, we consider special classes of strongly convex functionals in Sobolev spaces. It is proved that functionals from such classes have the so-called $H$-property: weak convergence of sequences of arguments and convergence of such sequences with respect to a given functional imply strong convergence.

DOI: https://doi.org/10.4213/mzm2500

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English version:
Mathematical Notes, 2005, 77:3, 348–363

Bibliographic databases:

UDC: 517.98
Received: 27.06.2002

Citation: A. S. Leonov, “On the $H$-property of functionals in Sobolev spaces”, Mat. Zametki, 77:3 (2005), 378–394; Math. Notes, 77:3 (2005), 348–363

Citation in format AMSBIB
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\pages 378--394
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Leonov, “On the total-variation convergence of regularizing algorithms for ill-posed problems”, Comput. Math. Math. Phys., 47:5 (2007), 732–747  mathnet  crossref  mathscinet  elib  elib
    2. A. S. Leonov, “Higher-order total variations for functions of several variables and their application in the theory of ill-posed problems”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 119–133  mathnet  crossref  isi  elib
    3. Korolev Yu., “Making Use of a Partial Order in Solving Inverse Problems: II.”, Inverse Probl., 30:8 (2014), 085003  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
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